Monday, June 10, 2013

Can cicadas calculate prime numbers?

Photo: Tom Wildoner

In the US the 17-year cicada hatch of 2013 is in full bloom. Millions of crimson-eyed critters and their otherworldly din, I've seen them described as. They showed up yesterday in Carbon County, Pennsylvania – the photo comes from EarthSky. These 17-year cicadas live out most of their long lives as nymphs underground, but, each 17 years, they crawl out of the ground for a three-to-four-week festival of singing and mating. Afterwards, they die. Why every 17 years? Because they are mathematicians, that’s why. They recognise 17 as a prime number and they use it to elude their predators.

It works this way. Cicadas are easy prey for birds and wasps. Now it turns out that predators commonly have 2-to-10-year population cycles. Imagine a cicada species with a 12-year cycle: it would be a feast for any predator with a 2-, 3-, 4-, or 6-year cycle (factors of 12).

On the other hand, Stephen J Gould reasoned in a famous essay that a cicada that emerges every 17 years and has a predator with a 5-year population cycle will only face a peak predator population once every 85 (5 x 17) years.

Advantage of prime numbers

This gives an enormous advantage to cicadas that know how to calculate prime numbers. Some biologists however claim that advanced number theory is well beyond the cicadas insect-sized brain and suggest instead that the pattern emerged as a result of Darwinian natural selection: cicadas that matured in easily divisible years were gobbled up by predators, and simply didn’t live long enough to produce as many offspring. Those who, by chance, had long, prime-numbered life spans fared best, survived longest, and left the most offspring, becoming the dominant variation of the species. It seems there are now at least fifteen distinct populations of periodical cicadas. Cicada emergence is tightly timed, with the bulk of the insects emerging within a span of a few weeks. Any cicada that tries to break the pattern is highly likely to have her offspring gobbled up.

I first became aware of this cicada prime number behaviour a few years ago through an In Our Time episode on prime numbers which I highly recommend. It included my guru Marcus du Sautoy.

In another radio programme I heard the biologist Simon Conway Morris pour cold water on cicadas and prime numbers, but he didn't elaborate his reasons.